$\vec{w}h\alpha\mathfrak{t}\;\; i\mathbb{S}\ldots$

the Atiyah-Singer Index Theorem?

Lucas Braune (IMPA Rio de Janeiro)
2014/06/27, 16:00
HU Berlin, at Rudower Chaussee 25, room 1.023
About what?

The Atiyah-Singer index theorem is a general result that gives an integral formula for the index of an elliptic operator on a compact manifold. It has as immediate corollaries, fundamental theorems in different areas of geometry --- theorems whose statements have seemingly nothing to do with an index. The main examples are the Chern-Gauss-Bonnet theorem, the Hirzebruch signature formula, and the Riemann-Roch-Hirzebruch theorem. My purpose for this talk is to show each of these theorems as a solution to an index problem and, with this as the motivation, to explain the statement of a version of the Atiyah-Singer index theorem.